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midterm_1_-_questions_Winter_2008

midterm_1_-_questions_Winter_2008 - ACTSC/STAT 446/846...

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ACTSC/STAT 446/846 – Midterm #1 – Winter 2008 (Version A - Section 3) Department of Statistics and Actuarial Science, University of Waterloo February, 2008 Name: Section: ( Please write your UWID number on the back of this page only. ) Duration: 50 minutes There are six questions for a total value of 40 points.
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2 of 10 Please write your ID here: Total: /40 (You can use this page for additional space if required)
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3 of 10 1. [total= 4 points] Suppose S t denotes the price of the stock at time t . Let r be the con- tinuously compounded risk-free interest rate. Today, S 0 = $45. Assume that there are no dividends. (a) [1pt] Express the forward price F for a forward contract with maturity T years as a function of the parameters of the problem: (b) [3pts] A forward contract with the obligation to buy at maturity T the stock at the forward price F (calculated in a)) is available on the market at a premium 7$ at 0 < t < T . Give an expression of the stock price at time t .
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4 of 10 2. [Total=8 points] Consider a binomial tree with u = 1 . 1, d = 0 . 9, time-steps of size 3 months, an initial stock price S 0 = 100, and a risk-free rate of 5% (annual rate, continu- ously compounded). Assume the stock pays no dividend.
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